This section succinctly exposes the precise theoretical conditions allowing to discern between SMEFT and HEFT, compiling the main results of several articles [1]}, [2]}, [3]}, [4]}, [5]} in their geometrical aspects and adding an extended analytical discussion about the function \(\mathcal {F}\)  of our own.
Much of the past confusion between the two EFT formulations arises from the fact that there are two coordinate systems to describe the same system of fields, for this, the San Diego group advocated for employing a geometric perspective to be able to make coordinate-invariant statements.
